Trie insertion and search in Data Structures Theory - Step-by-Step Execution

Concept Flow - Trie insertion and search

Insert/Search first char

↓

Node exists?

No→Create new node

↓

Link new node

↓

Move to next char

↓

Repeat until word end

↓

Mark end of word (insertion) or Return found/not found (search)

For each character in the word, check if a node exists. If not, create it. Move to the next character until the word ends. Mark the end for insertion or check for presence in search.

Execution Sample

Data Structures Theory

Insert 'cat'
Insert 'car'
Search 'cat'
Search 'cap'

Insert two words 'cat' and 'car' into the trie, then search for 'cat' and 'cap'.

Analysis Table

Step	Operation	Current Char	Node Exists?	Action	Trie State (Visual)
1	Insert	'c'	No	Create node 'c'	∅ → c
2	Insert	'a'	No	Create node 'a' under 'c'	c → a
3	Insert	't'	No	Create node 't' under 'a'	c → a → t (end)
4	Insert	'r'	No	Create node 'r' under 'a'	c → a → t (end), a → r (end)
5	Search	'c'	Yes	Move to node 'c'	c → a → t, a → r
6	Search	'a'	Yes	Move to node 'a'	c → a → t, a → r
7	Search	't'	Yes	Move to node 't'	c → a → t (end), a → r
8	Search	End of word	Yes	Word found (end marked)	c → a → t (end), a → r
9	Search	'c'	Yes	Move to node 'c'	c → a → t (end), a → r
10	Search	'a'	Yes	Move to node 'a'	c → a → t (end), a → r
11	Search	'p'	No	Node 'p' missing, word not found	c → a → t (end), a → r

💡 Search stops when all characters are found and end of word is marked, or when a character node is missing.

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	After Step 8	After Step 9	After Step 10	After Step 11
Current Node	Root (empty)	Node 'c'	Node 'a'	Node 't'	Node 'r'	Node 'c'	Node 'a'	Node 't'	End	Node 'c'	Node 'a'	None
Trie Size (nodes)	0	1	2	3	4	4	4	4	4	4	4	4
Word Found Flag	False	False	False	False	False	False	False	False	True	False	False	False

Key Insights - 3 Insights

Why do we create new nodes only when the character node does not exist?

Because existing nodes represent prefixes already stored. Creating new nodes only when missing avoids duplicates and keeps the trie compact, as shown in steps 1-4 of the execution_table.

How do we know a word ends in the trie?

We mark the last node of the inserted word as an 'end' node. During search (step 8), finding this mark confirms the word exists.

Why does the search fail at step 11 for 'cap'?

Because the node for character 'p' does not exist under 'a', so the trie cannot match the word fully, indicating 'cap' is not stored.

Visual Quiz - 3 Questions

Look at the execution_table at step 4. What is the trie state after inserting 'car'?

A c → a → t (end), a → r (end)

B c → a → r (end)

C c → a → t → r (end)

D c → r → a (end)

💡 Hint

Refer to the 'Trie State (Visual)' column at step 4 in the execution_table.

At which step does the search confirm the word 'cat' is found?

A Step 7

B Step 6

C Step 8

D Step 11

💡 Hint

Check the 'Word Found Flag' in variable_tracker and the 'Action' column in execution_table.

If we tried to insert 'cap' after 'cat' and 'car', what would happen at step 11?

A Search would fail at 'p'

B Node 'p' would be created under 'a'

C Node 't' would be replaced by 'p'

D Word would be marked as not found

💡 Hint

Insertion creates missing nodes; step 11 shows search fails because 'p' node is missing.

Concept Snapshot

Trie insertion and search:
- Insert: For each char, create node if missing
- Search: For each char, move if node exists
- Mark end of word on insertion
- Search success if all chars found and end marked
- Efficient prefix-based storage and lookup

Full Transcript

A trie stores words by creating nodes for each character. When inserting, we check if a node for the current character exists. If not, we create it and link it under the previous node. We repeat this for all characters and mark the last node as the end of a word. Searching follows the same path: for each character, we move to the corresponding node if it exists. If all characters are found and the last node is marked as an end, the word exists. If any character node is missing, the search fails. This method efficiently stores and searches words by their prefixes.